Answer
The fractional mass decrease is $1.29\times10^{-8}$.
Work Step by Step
The emitted photon carries away mass-energy. Calculate the energy of a photon falling from the n = 3 state down to n = 1 state in hydrogen.
$$\Delta E=E_3-E_1=-(13.6eV)(\frac{1}{3^2}-\frac{1}{1^2})=12.1eV$$
Calculate the fractional change.
$$\frac{\Delta m}{m}=\frac{E_{photon}}{mc^2}=\frac{12.1eV}{939\times10^6eV}=1.29\times10^{-8}$$